GATE CE
$$\int\limits_C {{{{z^3} - 6} \over {3z - i}}} dz$$ is where C is |z| = 1
$$1.$$ The modular ratio considered in the working stress method depends on the type of steel used.
$$2.$$ There is an upper limit on the nominal shear stress in beams (even with shear reinforcement) due to the possibility of crushing of concrete in diagonal compression.
$$3.$$ A rectangular slab whose length is equal to its width may not be a two-way slab for some support conditions.
The TRUE statements are
At the limiting state of collapse in flexure, the force acting on the compression zone of the section is
The depth of neutral axis for the balanced failure is
$$1.\,\,\,\,\,\,$$ The width-to-thickness ratio limitations on the plate elements under
$$\,\,\,\,\,\,\,\,\,\,\,$$ compression in steel members are imposed by $$IS:$$ $$800$$ - $$1984$$ in order to avoid
$$\,\,\,\,\,\,\,\,\,\,\,$$ fabrication difficulties.
$$2.\,\,\,\,\,\,$$ In a doubly reinforced concrete beam, the strain in compressive reinforcement is
$$\,\,\,\,\,\,\,\,\,\,\,$$ higher than the strain in the adjoining concrete.
$$3.\,\,\,\,\,\,$$ If a cantilever $${\rm I}$$-section supports slab construction all along its length with
$$\,\,\,\,\,\,\,\,\,\,\,$$ sufficient friction between them, the permissible bending stress in compression
$$\,\,\,\,\,\,\,\,\,\,\,$$ will be the same as that in tension.
The TRUE statements are
$${\rm I}.\,\,\,\,$$ Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns.
$${\rm II}.\,\,\,\,$$ As per $$IS:$$ $$800$$-$$1984,$$ permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel.
$${\rm III}.\,\,\,\,$$ As per $$IS:$$ $$800$$-$$1984,$$ the effective length of a column effectively held in position at both ends but not restrained against rotation, is taken to be greater than that in the ideal end conditions.
The TRUE statements are
$${\rm I}.\,\,\,\,\,\,\,\,\,$$ The entire cross-sectional area of the connected leg is assumed to contribute to the effective area in case of angles.
$${\rm II}.\,\,\,\,\,\,\,\,\,$$ Two angles back-to-back and tack-welded as per code requirements may be assumed to be behave as a $$T$$-section
$${\rm III}.\,\,\,\,\,\,\,\,\,$$ A check on slenderness ratio may be necessary in some cases.
The TRUE statements are

Where $$\alpha $$ is equal to

The reaction at $$C$$ is

The rotation at $$B$$ is





The beam is possibly under the action of following loads



